Question

question 7 of 24 step 1 of 1
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solve the following elementary exponential equation.
$2^x - 16 = 0$
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4 points

Explanation:

Step1: Isolate the exponential term

We start with the equation \(2^{x}-16 = 0\). To isolate the exponential term \(2^{x}\), we add 16 to both sides of the equation. This gives us \(2^{x}=16\).

Step2: Express 16 as a power of 2

We know that \(16 = 2^{4}\) because \(2\times2\times2\times2 = 16\). So we can rewrite the equation as \(2^{x}=2^{4}\).

Step3: Use the property of exponential functions

For an exponential function \(a^{m}=a^{n}\) (where \(a>0,a
eq1\)), we have \(m = n\). Since the base \(a = 2\) (which is greater than 0 and not equal to 1), we can set the exponents equal to each other. So \(x = 4\).

Answer:

\(x = 4\)